Given $ m \angle ABC = 9x - 29$, and $ m \angle CBD = 4x + 27$, find $m\angle ABC$. $B$ $A$ $D$ $C$
Explanation: From the diagram, we see that together ${\angle ABC}$ and ${\angle CBD}$ form ${\angle ABD}$ , so $ {m\angle ABC} + {m\angle CBD} = {m\angle ABD}$ Since $\angle ABD$ is a straight angle, we know ${m\angle ABD = 180}$ Substitute in the expressions that were given for each measure: $ {9x - 29} + {4x + 27} = {180}$ Combine like terms: $ 13x - 2 = 180$ Add $2$ to both sides: $ 13x = 182$ Divide both sides by $13$ to find $x$ $ x = 14$ Substitute $14$ for $x$ in the expression that was given for $m\angle ABC$ $ m\angle ABC = 9({14}) - 29$ Simplify: $ {m\angle ABC = 126 - 29}$ So ${m\angle ABC = 97}$.